Ukrainian Mathematical Journal

, 63:580 | Cite as

Properties of a certain product of submodules

  • M. J. Nikmehr
  • R. Nikandish
  • S. Heidari

Let R be a commutative ring with identity, let M be an R-module, and let K 1, . . . ,K n be submodules of M: We construct an algebraic object called the product of K 1, . . . ,K n : This structure is equipped with appropriate operations to get an R(M)-module. It is shown that the R(M)-module M n = M . . .M and the R-module M inherit some of the most important properties of each other. Thus, it is shown that M is a projective (flat) R-module if and only if M n is a projective (flat) R(M)-module.


Positive Integer Multiplication Module Prime Ideal Local Ring Maximal Ideal 
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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  • M. J. Nikmehr
    • 1
  • R. Nikandish
    • 1
  • S. Heidari
    • 1
  1. 1.Toosi University of TechnologyTehranIran

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